Increase/decrease the magnitude of the EMFs and the resistors by clicking
on the upper/lower part of the object. The values of the resistors range from
1 to 10 ohms. And the values of the EMFs range from -10 to +10 Volts.
The ammeters show the currents in the wires, the voltmeters show the voltages
across the resistors.
The circuit consists of a loop ABCDEF and the following components
attached to each of it's three branches: an EMF (except for branch C),
an Ammeter which measures the current through that branch, a resistor,
and a Voltmeter which measures the potential rise/drop on the
resistor. The values for each of the components can be seen either
next to or written on the components themselves. It should be made
clear that the Ammeters and Voltmeters are positioned in such a way
that they will show a positive reading when the current is flowing
from top to bottom, although such a selection is made in this circuit
it would have been just as correct to pick it's opposite.

These three basic rules/formulas are needed to solve the system of equations
envolved:

1. Kirchhoff's Junction Rule,

2. Kirchhoff's Loop Rule and

3. Ohm's Law (i.e. V/I = R,

where I is the current, V is the voltage, and R
is the resistance).

To solve the equations we will need to name our components, we have
chosen a system in which each component is named by a letter
indicating it's type (I for current, E for the
EMF, and R for resistance) and a subletter indicating it's
branch (A, B, or C). Thus the current in the leftmost branch would be
(by Ohm's Law):
IA = VA/RA.
Now we are ready to formulate the system.

First, we take the outer most loop ACDF and use the Junction
Rule. Let's take junction B, since we assume that all of the
currents flow from top to bottom, the sum of the currents heading out
of the loop is equal to zero (since no current is heading in) i.e.,
IA + IB + IC = 0.

Next we take loop ABEF and apply the Loop Rule, which says
that the sum of the potential rises must equal to the sum of the
potential drops i.e.,
EA + IA*RA =
EB + IB*RB;

we also apply this rule to the outer loop, ACDF, getting:
EA + IA*RA =
IC*RC.